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Despite massive investment and carbon-neutral transition goals set around the world, gasoline-based internal combustion engine vehicles still form an absolute majority in the transportation sector. With the advent of technology, access to electricity, uncertainties in fuel prices and health awareness, people worldwide are moving towards a better, reliable, cost-effective and environmentally friendly mode of transportation, a hybrid electric vehicle. Such a vehicle, with its powerful electric motor and compact gasoline-based engine, offers better efficiency in terms of operating cost and reliability. Considering the advent of hybrid electric vehicles taking pace, studies related to its architecture types, power flow dynamics, control and modelling of its various components will form an essential part of the automobile industry and research. This paper proposes a power flow topology for a hybrid electric vehicle with series-parallel architecture. The developed vehicle model with such an architecture type consists of three main sub-systems: the electrical system, the control system and the mechanical system. The presented power flow topology being modelled and analysed in detail in the Simulink tool is being implemented via a mode logic controller, which forms part of the central control system. The developed hybrid electric vehicle model demonstrates various modes of operation, from starting to accelerating to de-accelerating and then finally coming to a complete rest. Each mode yields and explains the following: the vehicle reference speed; the engine and generator turn functions on/off; the dc bus and battery voltage; the motor, battery, and generator current; the motor, generator, and engine speed; engine torque; engine power; throttle demand; and the vehicle's actual speed. The results thus obtained show that the waveforms associated with such topology, during its various modes of operation, are pretty stable and acceptable, thereby depicting and validating the operation of the developed hybrid electric vehicle model with proposed power flow topology in a precise and transparent manner. [ABSTRACT FROM AUTHOR]